Hi there, I hope your new girl is settling in well. We had this with our dog for some time when we first got him (supposedly as a "puppy" but he wasn't really). He would pee 'outside', but never poo.
I have no tips or solutions to suggest, but I just wanted you to know, in my experience it did pass, so there's hope. Praise her every time she goes to toilet, and perhaps put a command to it, then when you take her out of the house, you could try taking treats, and using the command while she is out. MASSIVE fuss if she 'goes'!
It isn't a massive deal right now, but I know that you may want to take her for days out, if that's the kind of thing you do, and obviously she can't be crossing her legs all day!
Lots of luck, and a cuddle for your girl. x